1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4

Slides:



Advertisements
Similar presentations
The Pythagorean Theorem and its Converse
Advertisements

Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.
Find hypotenuse length in a triangle EXAMPLE 1
EXAMPLE 4 SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of.
EXAMPLE 1 Find hypotenuse length in a triangle o o o Find the length of the hypotenuse. a. SOLUTION hypotenuse = leg 2 = 8 2 Substitute
EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.
The Pythagorean Theorem
EXAMPLE 2 Standardized Test Practice SOLUTION =+.
EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.
EXAMPLE 1 Find the length of a hypotenuse SOLUTION Find the length of the hypotenuse of the right triangle. (hypotenuse) 2 = (leg) 2 + (leg) 2 Pythagorean.
EXAMPLE 2 Standardized Test Practice SOLUTION =+.
11.2 Pythagorean Theorem. Applies to Right Triangles Only! leg Leg a hypotenuse c Leg b.
Slide #1.
7.1 The Pythagorean Theorem
About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.
Special Right Triangles 5.1 (M2). Pythagorean Theorem.
The Pythagorean Theorem
Chapter 7.1 & 7.2 Notes: The Pythagorean Theorem and its Converse
Quiz 1. Find the perimeter of the figure. 2. Find the area of the figure. 12 ft 4 ft5 ft 3. The perimeter of the triangle 4. The perimeter of the combined.
Special Right Triangles
Apply the Pythagorean Theorem
6-3 The Pythagorean Theorem Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.
Today’s Class Do now: – Work on Warm UP – Get out HW Objective – SWBAT apply the Pythagorean theorem to solve for missing side lengths – SWBAT apply the.
Warm Up: Find the geometric mean of: a) 12 and 18b) 54 and 36 c) 25 and 49.
1 The Pythagorean Theorem. 2 A B C Given any right triangle, A 2 + B 2 = C 2.
Things to remember: Formula: a 2 +b 2 =c 2 Pythagorean Theorem is used to find lengths of the sides of a right triangle Side across from the right angle.
1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4
EXAMPLE 4 Find the height of an equilateral triangle Logo
EXAMPLE 3 Use a geometric mean Find the value of y. Write your answer in simplest radical form. SOLUTION STEP 1 Draw the three similar triangles.
Special Right Triangles 5.1 (M2). What do you know about Similar Triangles?  Corresponding Angles are Congruent  Sides are proportional  Since the.
Warm-Up Exercises EXAMPLE 1 Find hypotenuse length in a triangle o o o Find the length of the hypotenuse. a. SOLUTION hypotenuse = leg 2 = 8=
OBJECTIVE I will use the Pythagorean Theorem to find missing sides lengths of a RIGHT triangle.
Warm-Up Exercises 2. Solve x = 25. ANSWER 10, –10 ANSWER 4, –4 1. Solve x 2 = 100. ANSWER Simplify 20.
9.2 The Pythagorean Theorem
11.2 Pythagorean Theorem. Applies to Right Triangles Only! leg Leg a hypotenuse c Leg b.
GEOMETRY HELP A right triangle has legs of length 16 and 30. Find the length of the hypotenuse. Do the lengths of the sides form a Pythagorean triple?
Special Right Triangles. Right triangles have one 90 o angle The longest side is called the HYPOTENUSE It is directly across from the 90 o The other sides.
SOLUTION Finding Perimeter and Area STEP 1 Find the perimeter and area of the triangle. Find the height of the triangle. Pythagorean Theorem Evaluate powers.
Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form Simplify expression. 3.
Geometry Section 7.1 Apply the Pythagorean Theorem.
EXAMPLE 3 Find the area of an isosceles triangle
Guided Notes/Practice
Warm Up Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = b = 21, c = a = 20, c = 52 c.
Warm Up Simplify the square roots
Find the geometric mean between 9 and 13.
1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4
Simplify ANSWER ANSWER 12 ANSWER
EXAMPLE 3 Use a geometric mean
Pythagorean Theorem and Its Converse
9.2 The Pythagorean Theorem
11.2 Pythagorean Theorem.
7.1 Apply the Pythagorean Theorem
The Pythagorean Theorem
Starter(s):.
Section 1 – Apply the Pythagorean Theorem
Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.
9-2 Pythagorean Theorem.
Objective - To find missing sides of right triangles using the Pythagorean Theorem. Applies to Right Triangles Only! hypotenuse c leg a b leg.
PROVING THE PYTHAGOREAN THEOREM
10.3 and 10.4 Pythagorean Theorem
Simplify ANSWER ANSWER ANSWER
7.1 Apply the Pythagorean theorem.
11.7 and 11.8 Pythagorean Thm..
The Pythagorean Theorem
Remember Rough Draft is due Quiz Corrections are due
The Pythagorean Theorem
Solve for the unknown side or angle x
Lesson 8-7 The Pythagorean Theorem
Splash Screen.
Presentation transcript:

1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4 3. Simplify 20. ANSWER 2 5

4. Find x. ANSWER 6 cm

Find the length of a hypotenuse EXAMPLE 1 Find the length of a hypotenuse Find the length of the hypotenuse of the right triangle. SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem x2 = 62 + 82 Substitute. x2 = 36 + 64 Multiply. x2 = 100 Add. x = 10 Find the positive square root.

GUIDED PRACTICE for Example 1 1. Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form. ANSWER Leg; 4

GUIDED PRACTICE for Example 1 2. Identify the unknown side as a leg or hypotenuse. Then, find the unknown side length of the right triangle. Write your answer in simplest radical form. hypotenuse; 2 13 ANSWER

EXAMPLE 2 Standardized Test Practice SOLUTION = +

Standardized Test Practice EXAMPLE 2 Standardized Test Practice SOLUTION 162 = 42 + x2 Substitute. 256 = 16 + x2 Multiply. 240 = x2 Subtract 16 from each side. 240 = x Find positive square root. 15.492 ≈ x Approximate with a calculator. ANSWER The ladder is resting against the house at about 15.5 feet above the ground. The correct answer is D.

GUIDED PRACTICE for Example 2 The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder? 3. about 23.8 ft ANSWER

GUIDED PRACTICE for Example 2 The Pythagorean Theorem is only true for what type of triangle? 4. right triangle ANSWER

EXAMPLE 3 Find the area of an isosceles triangle Find the area of the isosceles triangle with side lengths 10 meters, 13 meters, and 13 meters. SOLUTION STEP 1 Draw a sketch. By definition, the length of an altitude is the height of a triangle. In an isosceles triangle, the altitude to the base is also a perpendicular bisector. So, the altitude divides the triangle into two right triangles with the dimensions shown.

Find the area of an isosceles triangle EXAMPLE 3 Find the area of an isosceles triangle Use the Pythagorean Theorem to find the height of the triangle. STEP 2 c2 = a2 + b2 Pythagorean Theorem 132 = 52 + h2 Substitute. 169 = 25 + h2 Multiply. 144 = h2 Subtract 25 from each side. 12 = h Find the positive square root.

EXAMPLE 3 Find the area of an isosceles triangle STEP 3 Find the area. 1 2 (base) (height) = (10) (12) = 60 m2 1 2 Area = ANSWER The area of the triangle is 60 square meters.

GUIDED PRACTICE for Example 3 5. Find the area of the triangle. ANSWER about 149.2 ft2.

GUIDED PRACTICE for Example 3 Find the area of the triangle. 6. ANSWER 240 m2.

Find the length of the hypotenuse of the right triangle. EXAMPLE 4 Find the length of a hypotenuse using two methods Find the length of the hypotenuse of the right triangle. SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of the Pythagorean triple by 2, you get the lengths of the legs of this triangle: 5 2 = 10 and 12 2 = 24. So, the length of the hypotenuse is 13 2 = 26.

Method 2: Use the Pythagorean Theorem. EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Method 2: Use the Pythagorean Theorem. x2 = 102 + 242 Pythagorean Theorem x2 = 100 + 576 Multiply. x2 = 676 Add. x = 26 Find the positive square root.

GUIDED PRACTICE for Example 4 Find the unknown side length of the right triangle using the Pythagorean Theorem. Then use a Pythagorean triple. 7. 8. ANSWER 15 in. ANSWER 50 cm.

Daily Homework Quiz 1. Find the length of the hypotenuse of the right triangle. ANSWER 39

Daily Homework Quiz 2. Find the area of the isosceles triangle. ANSWER 1080 cm 2

Daily Homework Quiz 3. Find the unknown side length x. Write your answer in simplest radical form. ANSWER 4 13